CHAPTER 15

Estimating Biodiversity:Indices, Effort, andInference

Michael E. Meredith

Estimating biodiversity at particular sites and contrasting it among sites is a fun-damental undertaking of conservation biologists, especially those working in thefield doing inventories and prioritizing sites for protection. We have already touchedupon this topic: in chapter 1, What is biodiversity?, where you looked at samplesof spiders from different communities and used the results to explore speciesrichness, species diversity, and the similarity of communities. With samples of50 individuals, it was easy to do this manually. But most real studies involve muchlarger numbers of individuals and large numbers of species. For example, the studyby Longino et al. (2002) of ants in lowland rain forest at La Selva Biological Station,Costa Rica, involved 7 904 observations of 437 species. Collecting and identifyingthe specimens required a huge effort spread over several years, but the data analysiswas relatively fast, and was, of course, computerized.

Apart from keeping track of the data and adding up the number of species we havecollected, sophisticated software lets us:

. estimate the completeness of our list of species and the species richness of the site

. compare the species richness of different sites, even though different numbersof individuals were collected at each

. check estimates of diversity indices to see if they are affected by incomplete sampling

. explore the similarity of communities at different sites or at different times.

Several software packages are available to analyze these kinds of data sets, but herewe will introduce EstimateS, which is both freely available and one of the mostwidely used packages. Developing a facility with EstimateS (or similar software) is arequisite for learning how to manage the data side of biodiversity inventory work.

Objective

. To build on the concepts introduced in chapter 1, and to explore how they can beimplemented and extended with the software package EstimateS.

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Procedures

Defining the Community

To use species richness in practice, we need first to define the group of individualorganisms to be included. We usually limit it to a particular taxonomic group (e.g.spiders or birds) and a particular place (e.g. La Selva or Yellowstone NationalPark). Often we specify a trophic level (e.g. insectivores) or a guild (e.g. understoreygleaners).

Richness estimation means counting the number of species, treating all speciesequally, whether they are endangered endemics or invasive weeds, top predatorsor primary producers. This is only reasonable if the population is defined so thatspecies are actually reasonably similar. A good question to ask yourself is: If onespecies dropped out, would the other species be able to fill the gap? If the answeris clearly No, then you need to change the community definition, or abandon theidea of just counting species.

We can rarely study all the individual organisms in our target community, andwe usually have to work with samples. Invariably there will be population boundariesdefined by our sampling method: for the spiders in chapter 1, specimens werecollected by striking tree branches with a stick; you could not compare the resultsfrom these collections with an additional site where spiders had been collected fromthe leaf litter. Results can only be compared if the same sampling methods wereused in gathering the data.

Some of the rare species we encounter are actually edge species, on theboundary of our defined groups of organisms. For example, if we were using trapsbaited with fruit to study frugivorous butterflies in a forest, we might occasionallycapture a butterfly from the adjacent prairie (a spatial edge species), a nocturnalmoth (a temporal edge species), or a butterfly which does not feed on fruit(a methodological edge species). Deciding which to include can be difficult, as itimplies knowing what species ought to be present!

Bat Data from Loagan Bunut

The example data well use for the first part of this chapter are for bats caught in harptraps in peat swamp forest in Loagan Bunut National Park in Sarawak, Malaysia.

A harp trap has an aluminum frame with four parallel sets of vertical fishing lines(see Figure 15.1). A bat that flies into a harp trap will get caught in the fishing linesand slide down, uninjured, to the bag underneath. The bats are identified, weighed,measured, and released at the place they were captured at the end of the trappingsession. Harp traps are very efficient in capturing echo-locating bats, typically forestinterior species, which are unable to detect the thin lines of the harp trap.

Download the file LBunut_bats_input.txt from www.esf.edu/efb/gibbs/solving/.Open it in MS Excel1: either right-click on the file name and select Open With >MS Excel, or drag-and-drop the file into an open MS Excel window. (If you useFile > Open in MS Excel, the import wizard will start, which you dont need.)

The data file has a description of the data on the first line. On the second lineis the total number of species (22) followed by the number of samples (50). Thencome the records of bats captured, with a row for each species and a column foreach sample. Each sample corresponds to the bats caught on one night at one

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location. For example, the first column shows that on the first night 6 species werecaught (the other 16 rows contain 0), with one species represented by 2 bats andthe other 5 species represented by 1 bat each. The second sample had just 2 bats,both from the same species. (LBunut_bats_input.txt is formatted for input intoEstimateS. Note that EstimateS does not use species names or sample identifiers.)

Getting Started with EstimateS

Go to the EstimateS web site (http://purl.oclc.org/EstimateS), and fill in the regis-tration form. Then download the installer for the latest version of the software,currently EstimateS 8.0.0 in SetupEstimateSWin800.exe. As with any .exe file, itswise to save it on your hard disk, run a virus check with an up-to-date virus scanner,and create a Windows Restore Point before running the setup program. RunSetupEstimateSWin800.exe and follow the on-screen instructions. If you use theresults from EstimateS in any report or paper, please cite it as:

Colwell, R. K. 2006. EstimateS: Statistical estimation of species richness and shared speciesfrom samples. Version 8.0.0. Users Guide and application published at: http://purl.oclc.org/estimates.

Open EstimateS and click OK to agree not to distribute EstimateS commercially.In EstimateS, click on File > Load Data Input File (or press CtrlI). In the dialogbox, navigate to the file LBunut_bats_input.txt and click Open. A confirmationscreen appears with the title of the data set and the number of species (22) and

Fig. 15.1 A harp trap (aluminum frame with four parallel sets of vertical fishing lines) used tocatch bats in peat swamp forest in Loagan Bunut National Park, Sarawak, Malaysia. (Drawingby Jason Hon.)

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samples (50). Theres also a list of optional items: dont worry about these, as we canset options later. Then a dialog appears asking for the format of the input file.LBunut_bats_input.txt is Format 1 and there are no rows with sample informationor columns with species names.

You should then see a box telling you that the data have been loaded successfully.Go to Diversity > Diversity Settings. . . (or press CtrlT) and then to the Estim-ators tab. In the top section, click on the radio-button next to Use classic formulafor Chao 1 & Chao 2. Then go to the Other Options tab and check the box nextto Compute Fishers alpha, Shannon, & Simpson indexes. Leave the other settingsas they are and click on Compute. If a box appears asking if its OK to erase someold Diversity Statistics, click on OK.

A box pops up briefly with a progress bar, then a table of results appears.EstimateS produces a huge mass of figures, far too many to digest. They makemuch more sense if we use them to draw graphs, so export them from EstimateSand load into MS Excel1 (or other spreadsheet software, such as the OpenOfficesoftware (http://www.openoffice.org/), with a good graphics facility).

Click on the Export button at the bottom of the results window, or go to Diversity>Export Diversity Stats. Give the results file a suitable name, such as LBunut_bats_results.txt. Find the file LBunut_bats_results.txt in My Computer and eitherright-click and select Open With > MS Excel or drag and drop into an MS Excelwindow.

The results should now appear in the spreadsheet. Plotting will be simpler if youdelete the first few lines, so that the column headings appear in Row 1, then save it inMS Excels .xls format: highlight the first three rows of the spreadsheet and selectEdit > Delete. . . then Entire Row. The column headings should now be in Row 1.

Look at the tab for this spreadsheet near the bottom of the window. It has the samename as the .txt file we imported, LBunut_bats_results, which is too long for someof the procedures we want to use later. Right-click on the tab name, select Rename,and change the name to just Lbunut. Go to File > Save As. . . , change Saveas Type, at the bottom of the dialog box, to Microsoft MS Excel Workbook (*.xls).

Species Accumulation Curves

When we looked at the input data, we saw that the number of species observed (Sobs)was 22. The first question is: Have we captured all the species in the population?

In chapter 1, you used a collectors curve to answer this question, plotting thenumber of species versus number of individuals as more and more spiders wereadded to the sample. The solid line in Figure 15.2 is the species accumulation curve

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Fig. 15.2 An example species accumulation curve. (See text for details.)

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for Loagan Bunut bats, drawn in the same way as we collected more and moresamples. In EstimateS, this kind of curve is called a Species Accumulation Curve.

This curve is quite jagged, and the shape depends on the order of the samples.But if the samples are properly independent, the order of collection doesnt matter.We can remove the jaggedness by shuffling the order of the samples many times andaveraging the curves obtained, to produce the dotted line in the graph. EstimateShas already done this, shuffling the samples 50 times and taking the mean; the resultsare in column G [Sobs Mean (runs)] of the spreadsheet. Lets plot it.

In the MS Excel spreadsheet, highlight column B and column G:

. Individuals (computed)

. Sobs Mean (runs)

(Click on the B at the top of column B, then hold down the Ctrl key while clickingon the G at the top of column G.)

Start the Chart Wizard by clicking on the toolbar button or using Insert > Chart. . .

Step 1 : Under Chart Type: select XY (Scatter), then in Chart Subtype choose onewith lines without markers. Click Next.

Step 2 : Check that one curve is displayed with the x-axis running from 0 to 200.On the Series tab, you should have one series (Sobs Mean (runs) ), with Column B(Individuals) used as the x values. If all is in order, press Next.

Step 3 : In the Titles tab, put in suitable names, such as:

. Chart title: species accumulation curve

. Value (x) axis: No. of Individuals

. Value ( y) axis: No. of Species

Press Next.Step 4 : Select As New Sheet, and name it Species Accumulation Curve; click Finish.

Save your work (CtrlS).

The curve is not exactly jagged, but it isnt really smooth either. More shuffles of thesamples would be needed to make it properly smooth. But EstimateS has anotherway to do this, using an algorithm developed by Mao Chang Xuan to calculate thevalues we would get for an infinite number of randomizations: this is in column C[Sobs (Mao Tau)]. His algorithms also allow us to calculate the confidence intervaland those values are in columns D and E. Add these to the graph as follows.

Go to the Species Accumulation Curve graph and select Chart > Add Data. . .Click on the small icon at the right-hand end of the Range box. Now go to theLBunut results spreadsheet and highlight columns B through E:

. Individuals (computed)

. Sobs (Mao Tau)

. Sobs 95% CI Lower and Upper Bounds.

(Click on the B at the top of column B, then hold down the Shift key will clicking onthe E at the top of column E.)

Click on the icon at the right-hand end of the Add Data Range dialog box.Back in the Add Data dialog box, click OK. The Paste Special dialog box opens.

. We want to Add cells as New series, with Values (Y) in columns.

. Make sure that the boxes next to Series Names in First Row and Categories(X Values) in First Column are both checked.

. Click OK.

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Three new lines appear in the graph, the middle one being very close to the originalSobs curve but much smoother. The outer lines are the confidence limits letsmake them dotted lines, the same color as the Mau Tao curve: right-click on the topline and select Format Data Series. . . . On the Patterns tab, change Style to a dottedline and Color to the same color as the main line (pink). Click OK. Do the same forthe bottom line.

The species accumulation curve we have just plotted is clearly still climbing andshowing no signs of leveling out at an asymptote. It looks as though our coverageof species is still rather incomplete.

Singletons and Uniques

Singletons are species which are represented by a single individual in the collection.If our sampling has been really thorough, we will have caught all the species theretwice or more. Are there singletons among the bat species trapped at Loagan Bunut?

Go to the LBunut worksheet in MS Excel. Highlight cell D2 (just below theheading Sobs 95% CI Lower Bound), then go to Window > Freeze Panes. Nowscroll down and check the last value in the Singletons Mean column (column H).Youll see there are 8 singletons (out of 22 species in total), so our sampling is notvery thorough. Check also the number of doubletons: these are species representedby just two individuals in the collection.

If bats of a particular species tend to occur in groups, well get a few samples withseveral bats and lots of samples with none. In this case, the concept of uniques species which occur in only one sample is more appropriate than singletons.Duplicates are species which occur in just two samples. Check the number ofuniques and duplicates in the Loagan Bunut bat data.

Just as for the species accumulation curve, the trend in the numbers of uniquesand duplicates (or singletons and doubletons) may be more informative than thefinal numbers. Lets plot the graphs.In the LBunut spreadsheet in MS Excel,highlight columns B, H, J, L, and N, i.e:

. Individuals (computed)

. Singletons Mean

. Doubletons Mean

. Uniques Mean

. Duplicates Mean.

(Click on the B at the top of column B, then hold down the Ctrl key while clickingon H, J, L and N.)

Start the Chart Wizard by clicking on the toolbar button or using Insert > Chart. . .

Step 1 : Under Chart Type: select XY (Scatter), then in Chart Subtype choose onewith Lines without markers. Click Next.

Step 2 : Check that 4 curves are displayed with the x-axis running from 0 to 200. Onthe Series tab, you should have 4 series, with Column B (Individuals) used as the xvalues. If all is in order, press Next.

Step 3 : In the Titles tab, put in suitable names, such as:

. Chart title: singletons, doubletons, uniques and duplicates

. Value (x) axis: No. of Individuals

. Value ( y) axis: No. of Species.

Press Next.

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Step 4 : Select As New Sheet: and call it, say, Singletons, etc; click Finish. Saveyour work (CtrS).

The curves have been smoothed in the same way as the first species accumulationcurve we plotted: EstimateS has shuffled the samples 50 times and averaged theresults. The shuffling is random, so you will not get exactly the same results each time.

What would you expect to see? When you have only a few samples, youd expectlots of uniques and singletons; these curves reach a peak at about 30 individuals (89samples) and then start to decline. The duplicates and doubletons reach a peak a bitlater, and then also decline. The graph for the Loagan Bunut bats is odd, because theuniques and singletons then start to climb again, and go on climbing. Can you figureout whats happening here?

Estimating True Species Richness

Unless we have collected an enormous amount of data, we will have missed a fewrare species. Estimates of species richness based on the number of species observed(Sobs) are generally too low. Can we use the data we have to estimate how manyspecies we have missed and what the true number might be?

Many people have suggested estimation methods, but there is no clearly correctway to estimate the true species richness from a sample. We are trying to extrapolatefrom what we know to a situation for which we have no data. The methods suggestedcan be grouped as follows:

. Jackknife and bootstrap methods examine the sampling process, asking, Howmany species which we know are there would we have missed if we had taken fewersamples, or different samples? This is then used to estimate the number missingfrom the actual set of samples.

. Anne Chaos methods consider the number of species which are so rare that theyonly occur once or twice in the sample, and try to estimate how many are evenrarer, so didnt turn up in the sample at all. ACE and ICE (Abundance-based andIncidence-based Coverage Estimators) use the same approach but using specieswhich occur 110 times in the sample.

. Finally, we can try to fit a mathematical equation to the species accumulationcurve, and use this to predict the number of species where the curve levels off.A favourite is the MichaelisMenton equation.

More details of these estimators are in the documentation for EstimateS, which youcan access on-line at http://purl.oclc.org/EstimateS.

What are the criteria for a good estimator of species richness? If an estimator givesthe correct values for the true richness based on the set of samples we have, thatvalue should not change as we add more samples. Plotted with the species accumu-lation curve, the ideal estimator would be a horizontal line which meets the speciesaccumulation curve where it levels off like the solid horizontal line in Figure 15.3.In practice, wed expect the estimate to be very imprecise when we have only observeda small number of individuals, but to settle down to the correct value as we observemore the dotted line in the graph would be fine. What we often get, however, is anestimate which climbs steadily as we collect more samples, like the dashed line; thisleaves us with the same problem we dont know where it will level off!

EstimateS calculates several estimates of true species richness. Lets plot them andsee if any fit our criteria for a good estimator.

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Plotting Estimators of Richness

In the LBunut spreadsheet in MS Excel, highlight the following columns:

. B Individuals (computed)

. C Sobs (Mao Tau)

. P ACE Mean

. R ICE Mean

. T Chao 1 Mean

. X Chao 2 Mean

. AB Jack 1 Mean

. AD Jack 2 Mean

. AF Bootstrap Mean

. AI MMMeans.

Start the Chart Wizard and plot a chart as you did for the singletons, uniques, etc.curve. (If you get a message saying Your formula contains an invalid externalreference. . . , it may be because the name of the results spreadsheet is too long.)Place the chart in a new spreadsheet and give it a title such as Species RichnessEstimators. Save your work.

The chart is a bit messy with so many lines, and the different colors in the legendare not clear. But if you point to a curve with your mouse, a small box appears withdetails of the data source. As youll see, most of the curves are climbing gradually,running parallel to the Sobs curve (the lowest one in the graph). Chao 1 and Chao 2are climbing more steeply; these are based on the numbers of singletons anddoubletons (Chao 1) or uniques and duplicates (Chao 2) and we saw earlier thatthese are anomalous. The only one which seems to be reasonably horizontal isMMMeans, the MichaelisMenton estimator based on the Mao Tau curve forSobs.

The MichaelisMenton equation describes the progress of an enzyme-catalyzedchemical reaction. There is no theoretical reason to think it might also describespecies accumulation, but it does have the right sort of shape, rising quickly at firstand then leveling out. The equation is quite simple:

Sobs Smax n

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Fig. 15.3 Two contrasting outcomes of attempts to estimate true species richness: an idealestimator would quickly level off (upper line); many estimators continue to climb as moreindividuals are collected and the end point is uncertain (lower curve). (See text for details.)

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where Smax is the maximum number of species where the curve levels off, n is thenumber of individuals in the set of samples so far, and B is the number of individualsneeded to get half the maximum number of species, i.e. when nB, Sobs Smax=2.The MMMeans column gives us the estimate of Smax as we add more samples to thesample set. With all the available samples, the best-fitting curve has Smax 24:57(look at the last value in the MMMeans column) and B 35.5 approximately (lookdown the Individuals column in the LBunut worksheet to find the value corres-ponding to Sobs 24.57/2 12.28 species). Lets plot this curve and see for our-selves if it looks like the species accumulation curve:

Insert a new column next to MMMeans (highlight the column to the right ofMMMeans, then use Insert > Column) and call it, say, MM fitted. In the first rowof data type

24:57 B2=(35:5 B2)

24.57 and 35.5 are the values for Smax and B, while the value in cell B2 is the numberof individuals, n. Select all the cells in this column from Row 2 to Row 51, then pressCtrlD to copy the formula to all the cells in the column. Save.

Now plot the MM fitted curve and the Sobs curve and the MMMeans curvetoo for good measure: Highlight columns:

. B Individuals (computed)

. C Sobs (Mao Tau)

. AI MMMeans

. AJ MM fitted

Start the Chart Wizard and plot a chart as before. Place it in a new worksheet with atitle such as MM curve. Save.

The MM fitted and Sobs curves are very close together on the left of the graph,but above about 120 individuals they start to diverge. The MM fitted curve willeventually level off at 24.57 species, but the Sobs curve looks as if it is headinghigher. The MichaelisMenton curve does not appear to be a good fit for the partof the curve we are interested in.

Comparing Species Richness Between Sites

Very often the important question is not How many species. . . ? but Are theremore species at. . . than. . . , either comparing two sites or the same site at twopoints in time. Here we can make inferences based on interpolation, which is muchsafer than extrapolation.

Some harp-trapping has been done in peat swamp forests at Maludam NationalPark, about 450 km from Loagan Bunut. Unlike Loagan Bunut, Maludam was usedfor timber production before being established as a national park. In Maludam,81 bats from 11 species were caught. In Loagan Bunut NP we caught 174 bats from22 species. Does that mean that Loagan Bunut has more species of bats which can betrapped in harp-traps?

We cant compare the species totals 11 vs 22 directly, because the number ofbats caught in Maludam is less than half the number caught in Loagan Bunut. If wehad carried on trapping at Maludam, we would almost certainly have found morespecies but, as weve seen, its difficult to estimate how many more. However, we canestimate how many species we would expect to find at Loagan Bunut if we onlytrapped 81 individuals. We use a subset of the data we collected at Loagan Bunut,

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with a process known as rarefaction. This involves taking samples at random fromthe Loagan Bunut set until we have approximately 81 individuals, and noting howmany species we have found. We do this many times, and average the number ofspecies.

In fact, the smoothing process for the species accumulation curve also usesrandom selections from the samples, and Rarefaction Curve is an alternative namefor the smoothed species accumulation curve. So the figures we need are already inthe output from EstimateS:

Go to the results spreadsheet for Loagan Bunut, and look down the Individuals(computed) column to find the number nearest to 81. Note the number of species Sobs (Mao Tau) and the upper and lower 95% confidence limits. With 23 sampleswed catch on average 80.04 individual bats, which is the nearest value to 81. Andwith 23 samples wed record on average 16.55 species. This is more that the 11species we recorded in Maludam NP with a very similar number of bats, so it appearsthat Loagan Bunut is indeed richer.

Now look at the 95% confidence intervals for Sobs for 23 samples: from 10.54 to22.55. The value of 11 lies within the 95% confidence interval, meaning that finding11 species (or even fewer) in 23 samples from Loagan Bunut is not improbable.

Simpsons Index: An Alternative to Species Richness

Species richness is a seductive concept, but it is almost impossible to measure. Wecan rely on getting the common species in our sample, its the rare species which arethe problem. Moreover, rare species are less important to the structure and functionof an ecosystem that the common species. (If thats not true of the community youhave in mind, you may need to revise how you define it.) So why not use a measurewhich depends mainly on the number of common species and is not changed muchby the number of rare species?

Several diversity indices do just that, including Simpsons Reciprocal index, whichyou met in chapter 1. Most indices are still biased low when calculated from samplesthat do not include all the species present in the population, but the bias is small.The original form of Simpsons index for samples (Simpson, 1949) was:

D X ni(ni 1)

N (N 1)

where ni is the number of individuals of species i in the sample and N is the totalnumber of individuals in the sample. When the ni values are all very large, this isequivalent to the simplified equation used in chapter 1; for small values of ni, theformula above gives unbiased estimates of the value for the whole population, andthe reciprocal of this is used by EstimateS.

Go back to the LBunut spreadsheet and look for the column headed SimpsonMean. (Note that EstimateS does not calculate Simpsons index by default, only ifyou check the box next to Compute Fishers alpha, Shannon, & Simpson indexes,on the Other Options tab in Diversity > Diversity Settings. . . , before running theanalysis.)

The values shown for Simpson are actually the Reciprocal Simpson index, 1/D. Theresult based on all the samples together is just over 11, which we can think of asindicating that there are 11 common species in Loagan Bunut peat swamps.

Do we have a big enough data set to get a good estimate of Simpsons index, orwill it continue to creep up as we collect more bats and discover more species? Well

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plot Simpsons index in the same way as the other results: in the LBunut spread-sheet, highlight the Individuals (computed) and Simpson Mean columns and plot agraph as we did before for the species accumulation curve and the species richnessestimators.

As you will see, the curve rises very quickly to a value above 10 and then soonsettles down near the final value of 11. Unlike the species richness estimators,Simpsons index is not much affected by the size of the sample set. EstimateScalculates two other indices: Fishers Alpha index and Shannons index. If you havetime, plot these, too, and see how they behave.

Estimating Site Similarity

In chapter 1, you used the Jaccard coefficient of community similarity to contrastpairs of sites, calculating the value based on samples of spiders from the differentsites. If sampling is incomplete, we will have missed some species in the communi-ties, and we will have underestimated the number of shared species. EstimateScan calculate the Jaccard coefficients and a range of more sophisticated similaritymeasures which aim to minimize the effect of incomplete sampling.

The harp-trapping techniques used in peat swamp forests in Loagan Bunut andMaludam were also deployed in lowland forest in Loagan Bunut. Table 15.1 belowsummarizes the results for the three sites.

Download the file bats_3sites_input.txt, which has these data formatted forinput to EstimateS. Open EstimateS and import the data. Now go to the SharedSpecies menu and select Shared Species Settings. . . . Check the box next to Computebootstrap SEs. . . , leave the other settings as they are, then press Compute. If a boxappears asking if its OK to erase some old Shared Species Statistics, click on OK.You can export the results to MS Excel if you wish, but there is nothing here whichwe can display as graphs.

Remember that comparisons are made between pairs of sites, so the three rows ofoutput correspond to:

1 vs 2 : Maludam peat swamp vs Loagan Bunut peat swamp1 vs 3 : Maludam peat swamp vs Loagan Bunut lowland forest2 vs 3 : Loagan Bunut peat swamp vs Loagan Bunut lowland forest.

Columns 3 and 4 show the number of species recorded in each of the two sites, andthen (column 5) the number of species record in both sites.

Next come estimates of the true number of species for the two sites using theACE estimator that we saw on page 147. If you look at the LBunut spreadsheetand check the last value in the ACE Mean column you will see it is the same as thevalue for ACE for Site 2. ACE uses details of the rare species included in thesample to estimate the number of rare species not included. The next column,Chao Shared Estimated uses the same approach to estimate the true number ofshared species. For more details, you can refer to the EstimateS documentation.It would be possible to plug these three estimates into the equation for the Jaccardcoefficient to get an estimate of its true value, but there are better solutions, as wellsee below.

In the next column, the Jaccard Classic result is the same as the Jaccard coefficientyou used in chapter 1:

number of shared species, Sshared=Stotal , the total number of species

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The Srensen Classic index is similar to the Jaccard coefficient, but uses the averagenumber of species in the two communities (or samples):

number of shared species, Sshared=Saverage, the average number of species

The Jaccard and Srensen indices give similar results, and there is a simple rela-tionship between them as shown in Figure 15.4. What we say about the Jaccardindex in the next few paragraphs applies also to the Srensen index.

Chao et al. (2005) made two suggestions to get around the problems caused byincomplete sampling. Incomplete sampling affects rare species, and the first lineof attack is to give more weight to abundant species than to rare species. Instead ofusing just the number of shared species, we use the proportion of individuals in eachsample belonging to shared species. For sample X,

UX total individuals belonging to shared species=total individuals in all species

Table 15.1 Results for harp-trapping techniques at three sites.

1. Maludampeat swamp

2. Loagan Bunutpeat swamp

3. Loagan Bunutlowland

Balionycteris maculata 0 4 0Cynopterus brachyotis 0 0 2Emballanura alecto 0 1 0Glischropus tylopus 0 1 1Hipposideros bicolor 0 1 0Hipposideros cervinus 7 18 0Hipposideros cinaraceus 0 0 1Hipposideros diadema 0 1 3Hipposideros dyacorum 0 4 16Hipposideros galeritus 0 1 1Hipposideros ridleyi 0 6 4Hipposideros sabanus 0 1 2Kerivoula hardwickii 4 14 14Kerivoula intermedia 13 14 21Kerivoula lenis 4 0 1Kerivoula minuta 16 6 10Kerivoula papillosa 12 16 27Kerivoula pellucida 11 25 26Macroglossus minimus 1 0 1Megaderma spasma 1 0 0Murina cyclotis 0 1 1Murina rozendaali 0 1 1Murina suilla 3 2 6Nycteris javanica 0 3 7Pipistrellus tenuis 0 0 2Rhinolophus acuminatus 0 0 1Rhinolophus arcuatus 0 0 1Rhinolophus borneensis 0 0 2Rhinolophus creaghi 0 25 0Rhinolophus sedulus 0 22 7Rhinolophus trifoliatus 9 7 5

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and Chaos Abundance-Based Jaccard index is then:

UAUB=(UA UB UAUB)

Fortunately, EstimateS does the calculation for us: see the column headedChao-Jacc-Raw-Abundance. The values here are higher than Jaccard Classic, showingthat it is the relatively abundant species which are shared.

The second step is to estimate the number of rare species missing from thesamples, based on details of the species which were found, and to use this to correctthe abundance-based index. The values are in the column headed Chao-Jacc-Est-Abundance. They are a little higher, if any, than the Raw versions, because theindex is in any case not very sensitive to rare species. EstimateS also estimates aStandard Error for the corrected index.

A similar series of indices based on the classic Srensen index is produced. Theequations are somewhat different, but the principles are the same. The last twocolumns show two well-known abundance-based similarity indices:

. The Morisita-Horn index compares the proportional abundances of the speciesin each sample, and is given by:

PpiApiB

12 (

Pp2iA

Pp2iB)

where piX is the proportion of species i in sample X (and is zero if the species isabsent).

. The Bray-Curtis index uses the raw numbers:

PniMIN

12 (NA NB)

where niMIN is the smaller of niA or niB, the number of individuals of species iin samples A and B (and is zero if the species is absent from either sample), and NAand NB are the total number of individuals in the two samples.

Compare the results in the last two columns. Remember that the Maludam sampleis about half the size of the others (81 bats vs. 174 and 163) simply because lesstrapping was done there, and this might affect the results of the Bray-Curtis index.

Finishing Off

EstimateS automatically saves the last set of data to be imported and the last set ofresults generated, which is useful if something goes wrong. But you should carefully

0.8

0.4

0.0

0.0 0.4 0.8

Jaccard

Sore

nsen

Fig. 15.4 Relationship between the Jaccard and Srensen indices of community overlap.

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keep the input data files and exported results if you wish to preserve them. CloseEstimateS by selecting File > Exit or click on the button in the top right cornerof the main EstimateS window.

Expected Products

. A presentation (in written, verbal, or presentation form as your instructor prefers)of your conclusions about the species richness of bats in the peat swamp forestsin Loagan Bunut National Park. If you think you can give a good estimate of theactual number of species of harp-trappable bats, give your estimates and justifythem. If not, explain why none of the values produced by EstimateS seems verygood. How can we get better estimates of the actual number of species?

. Use rarefaction to compare the species richness of Loagan Bunut peat swampswith Maludam peat swamps and Loagan Bunut lowland forest (where 163 bats of25 species were trapped). Calculate the Reciprocal Simpsons index of diversityfor the two additional sites, and see if the results agree with the rarefactionanalysis. (You can calculate the index from the figures in the table above, or youcan download the files Maludam_bats_input.txt and Lowland_bats_input.txt, anduse EstimateS.)

. Summarize the results of the analysis of similarity between the three commu-nities of harp-trappable bats. Which measures of similarity do you considermost appropriate for these data? (Hint: the main question is: Which pair ofcommunities is most similar?)

. Responses in a form indicated by your instructor to the Discussion questionsbelow.

Discussion

1 What are possible explanations of the shape of the curves for uniques and singletonsfor Loagan Bunut peat swamp bat? How would you test your hypotheses?

2 Mist nets were used at Maludam as well as harp traps, and the results are shownbelow in Table 15.2. How does this information affect the comparison betweenthe sites?

Table 15.2

Mist netting in Maludam

Balionycteris maculata 3Cynopterus brachyotis 32Kerivoula papillosa 1Kerivoula pellucida 1Macroglossus minimus 9Nycteris javanica 2Penthetor lucasii 1Rhinolophus trifoliatus 7

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3 Select two local conservation issues, one where species richness would be a goodcriterion for decision-making and one where it would result in a poor decision.In the latter case, what other factors would you need to consider as well as just thenumber of species?

Further Resources

The documentation of EstimateS explains in detail how the various results arecalculated; it is available online at http://purl.oclc.org/EstimateS.

Gotelli and Colwell (2001) give a good review of the issues involved in estimatingspecies richness and using species accumulation curves and OHara (2005) lookscritically at some of the underlying concepts. The study of ants by Longino et al.(2002) is a good example of the application of these concepts, and Kingstone et al.(2003) have done a major study of bat diversity. Magurran (2004) is a general referenceon biodiversity measures, and Hill (1973) describes a framework which shows howseveral of the common biodiversity indices are related.

The Clear Lake case study (Hunter & Gibbs, 2007, page 30) illustrates the dangersof using the number of species as the sole criterion for management decisions.

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